A pulley of radius \( 2 \mathrm{~m} \) is rotated about its axis by a force \( F=\left(20 t-5 t^...

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A pulley of radius \( 2 \mathrm{~m} \) is rotated about its axis by a force \( F=\left(20 t-5 t^{2}\right) \) newton (where \( t \) is measured in seconds)
\( \mathrm{P} \) applied tangentially. If the moment of inertia of the pulley

W about its axis of rotation is \( 10 \mathrm{~kg} \mathrm{~m}^{2} \), the number of rotations made by the pulley before its direction of motion is reversed, is
(1) less than 3
(2) more than 3 but less than 6
(3) more than 6 but less than 9
(4) more than 9
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